I don't understand what I'm even supposed to do with it? Most people put installation instructions somewhere lol but I've checked all your game related pages and can't find a way to play with the dlc
(also sorry if I'm coming off abrasive. I'm just frustrated. I've had the DLC installed a while yet have been continuously unable to play. I've also seen you tell people to follow the installation guide yet I have still been able to find an installation guide despite looking)
The installation guide is shown on this Itch page (above the comment section), and on a separate page once you've downloaded the DLC. If you've purchased the DLC, you would have also received similar instructions via email.
From the looks of your screenshot, you'll likely need to manually download the DLC (i.e., not through the Itch app), unzip it, then place the "14 Nights With You" folder inside the base game's "game" folder.
Since I don't use the Itch app, I can't really offer much help outside of this.